Gauged Supergravities in Various Spacetime Dimensions

Abstract

In this review articel we study the gaugings of extended supergravity theories in various space-time dimensions. These theories describe the low-energy limit of non-trivial string compactifications. For each theory under consideration we review all possible gaugings that are compatible with supersymmetry. They are parameterized by the so-called embedding tensor which is a group theoretical object that has to satisfy certain representation constraints. This embedding tensor determines all couplings in the gauged theory that are necessary to preserve gauge invariance and supersymmetry. The concept of the embedding tensor and the general structure of the gauged supergravities are explained in detail. The methods are then applied to the half-maximal (N=4) supergravities in d=4 and d=5 and to the maximal supergravities in d=2 and d=7. Examples of particular gaugings are given. Whenever possible, the higher-dimensional origin of these theories is identified and it is shown how the compactification parameters like fluxes and torsion are contained in the embedding tensor.

155 pages, author's PhD thesis

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• The gauge structure of Exceptional Field Theories and the tensor hierarchy
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• The tensor hierarchy algebra
• The general gaugings of maximal d=9 supergravity
• The tensor hierarchy simplified
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• Tensor Hierarchies of 5- and 6-Dimensional Field Theories
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• $L_{\infty }$ algebras and Tensor Hierarchies in Exceptional Field Theory and Gauged Supergravity
• Maximally Supersymmetric AdS Solutions and their Moduli Spaces
• Critical points of maximal D=8 gauged supergravities
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• Higher Gauge Theory
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• Exotic potentials and Bianchi identities in SL(5) exceptional field theory
• On gauged maximal d=8 supergravities
• A Massive S-duality in 4 dimensions